Abstract
In the current article, a combination of the differential transform method (DTM) and Padé approximation method are implemented to solve a system of nonlinear differential equations modelling the flow of a Newtonian magnetic lubricant squeeze film with magnetic induction effects incorporated. Solutions for the transformed radial and tangential momentum as well as solutions for the radial and tangential induced magnetic field conservation equations are determined. The DTM-Padé combined method is observed to demonstrate excellent convergence, stability and versatility in simulating the magnetic squeeze film problem. The effects of involved parameters, i.e. squeeze Reynolds number (N 1), dimensionless axial magnetic force strength parameter (N 2), dimensionless tangential magnetic force strength parameter (N 3), and magnetic Reynolds number (Re m) are illustrated graphically and discussed in detail. Applications of the study include automotive magneto-rheological shock absorbers, novel aircraft landing gear systems and biological prosthetics.
Highlights
Understanding magneto-hydrodynamics (MHD) is strongly related to the comprehension of physical effects which take place in MHD
The nonlinear ordinary differential equations subject to the boundary conditions are solved via differential transform method (DTM)-Padé method for some values of the four key parameters i.e. squeeze Reynolds number (N1), magnetic Reynolds number (Rem = N1 Batchelor number (Bt)), dimensionless axial magnetic force parameter (N2), dimensionless tangential magnetic force parameter (N3) on the velocity and induced magnetic field components in the gap between the disks and on the torques at the lower and upper disk
The magnetic Reynolds number defines the ratio of the fluid flux to the magnetic diffusivity
Summary
Understanding magneto-hydrodynamics (MHD) is strongly related to the comprehension of physical effects which take place in MHD. Bég et al [22] analyzed the magneto-hydrodynamic squeezing flow of a microstructural fluid in a porous media biological bearing with the Liao homotopy analysis method (HAM), observing that micro-rotation of lubricant micro-elements is strongly influenced by Hartmann number and medium permeability, and that response time is enhanced with magnetic field. In the present article we employ DTM-Padé method to analyse two nonlinear magneto-hydrodynamic squeeze film boundary value problems. In this problem, we assume the axisymmetric flow in a polar coordinate system (r, θ, z) of a thin Newtonian, hydro-magnetic lubricant fluid squeeze film between two disks placed parallel to each other and each rotating at constant velocity in its own plane. The value of m is decided by convergence of the series coefficients
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